My dad put our only TV out with the trash because it would not turn on. It was a tube B&W model and I fixed it by soldering the power cord directly to the chassis, bypassing a bad connector on the rear panel. I put it in my bedroom and claimed it as mine since it was in the trash. My dad let me keep it for a couple days until my 5 siblings complained. I was 10 at the time.
The only game I had in middle school for PC that wasn't education focused was Star Wars Empire at War. I ended up learning how to modify the files to change things like unit stats, unit cap, faction, etc.
In particular I remember deciding that every space ship should be it's own unit instead of the squad being a unit and ramping the unit cap up to a crazy high number then having giant space battles. Also I really liked the pirate units so I think I gave those to both the Empire and the Rebels.
Early in my computer education at high school, I took a PET maze generator from one game, It was in ML and I didn't know ML, only the SYS to start it and how to use the ML monitor to SAVE the game to preserve the code. Added in a 4 way scrolling type-in ML routine from a magazine, and some BASIC game code which created a moving maze game where the maze moved around the stationary player.
I don't know if this qualifies as hack, but as a kid I was pretty proud about changing the code of qbasic's nibble.bas to get infinite lives. If I remember correctly it lead to some further experiments (snake's length, level editing) and eventually I managed to break it completely.
Modifying strings in the GUI using ResEdit back in the Mac OS 7-9 days. It was quite fun to change the title of a scoreboard to your name or increase a default variable size.
One that sticks with me the most early on was very simple but inspiring. Using a hole punch to turn a single sided floppy disk into a double sided at a time when double sided cost more.